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Activity Number: 56 - Novel Statistical Methods for Variable Selection with Applications
Type: Topic Contributed
Date/Time: Sunday, July 29, 2018 : 4:00 PM to 5:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #330806 Presentation
Title: Weak Signals in High-Dimension Regression: Detection, Estimation and Prediction
Author(s): Yi Li*
Keywords: high-dimensional data; lasso; post-selection shrinkage estimation; weak signal detection

Regularization methods, including Lasso, group Lasso and SCAD, typically focus on selecting variables with strong effects while ignoring weak signals. This may result in biased prediction, especially when weak signals outnumber strong signals. This paper aims to incorporate weak signals in variable selection, estimation and prediction. We propose a two-stage procedure, consisting of variable selection and post-selection estimation. The variable selection stage involves a covariance-insured screening for detecting weak signals, while the post-selection estimation stage involves a shrinkage estimator for jointly estimating strong and weak signals selected from the first stage. We term the proposed method as the covariance-insured screening based post-selection shrinkage estimator. We establish asymptotic properties for the proposed method and show, via simulations, that incorporating weak signals can improve estimation and prediction performance. We apply the proposed method to predict the annual gross domestic product (GDP) rates based on various socioeconomic indicators for 82 countries.

Authors who are presenting talks have a * after their name.

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